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Electrochemistry studies how chemical reactions, transport, and chemical equilibrium couple to electric charge and electric potential. In a cell, Electrons travel through the external circuit, while mobile ions carry electric current through the electrolyte. At the electrodes, redox reactions connect these two forms of electric charge transport. This connection makes it possible both to obtain electrical work from a chemical reaction and to use electrical work to drive a chemical reaction.

An anode is an electrode where oxidation occurs; a cathode is an electrode where reduction occurs. These definitions refer to the chemical reactions, rather than universal positive or negative terminal signs. In a galvanic cell delivering electrical work, the anode is negative and the cathode positive. In an electrolytic cell driven by an external source, the anode is positive and the cathode negative. See Pingarrón et al., Terminology of electrochemical methods of analysis (IUPAC Recommendations 2019), §§3.1 and 3.4 and Flowers et al., Chemistry 2e, §17.2: galvanic cells.

For a worked example, consider an electrolytic cell containing molten sodium chloride, with the anode connected to the positive terminal and the cathode to the negative terminal of an external source. At the cathode, sodium cations gain Electrons; at the anode, chlorine anions lose Electrons:The first line has net electric charge zero on each side; the second has $-2e$ on each side. Adding the lines cancels the transferred Electrons and preserves both chemical atom counts and net electric charge. The sodium product is neutral, and the chlorine product is a diatomic molecule. These equations specify molten sodium chloride; aqueous chemical solutions introduce competing water reactions. See 17.7 Electrolysis (§17.7: electrolysis of molten sodium chloride).

Electrochemistry underlies battery charging and the manufacture of chemicals by electrolysis. Its particularly useful idea is that an Electron inventory in a balanced chemical equation also accounts for transported electric charge. Transport alone is a different question from an electrode chemical reaction: an ion may carry electric current through the electrolyte without itself being consumed at an electrode.

Historically, Michael Faraday introduced the terms electrode, electrolyte, anion, cation, and ion in the terminology section of his 1834 paper, Experimental Researches in Electricity, Seventh Series by Michael Faraday (§§662–667). His §667 explicitly treats the direction assigned to electric current as a convention. His ion language predates the modern Electron and atomic nucleus picture used in the charge-counting example above.

For an electrolyte near chemical equilibrium, a Poisson-Boltzmann equation can approximate the distribution of ions in an electric potential. Such an equilibrium model does not by itself describe a cell carrying sustained electric current.

Faraday's laws of electrolysis state that the mass of material formed or consumed by a specified electrode reaction is proportional to the transported electric charge, and that equal electric charge produces masses proportional to $M/z$ for different reactions. Here $M$ is the product's mass per mole, and $z$ is the positive number of Electrons transferred per product entity. For complete use of the electric charge in that reaction,The first relation uses the Faraday constant; the second uses half-reaction stoichiometry; the third converts amount of substance to mass. For equal transported electric charge in two ideal cells,The number $z$ belongs to the balanced half-reaction, rather than to the metal's name alone: copper deposited from ${\mathrm{Cu}}^{2+}$ needs $z=2$. These modern forms of both laws are given in KIT's practical.^[ref]

If other same-direction electrode reactions share the measured electric current, define an integrated current efficiency $\eta =Q_{\mathrm{product}}/Q$. Provided the product is neither subsequently consumed nor lost, the retained mass isHere $0\le \eta \le 1$ follows from the specified same-direction partition of electric current. It is not a universal bound on every signed partial-current convention: IUPAC notes that simultaneous oxidation and reduction at one electrode can produce a current-efficiency ratio above one.^[ref] When efficiency varies during a run, use the charge-weighted ratio above, rather than an unweighted average over time. If deposition removes material from a multicomponent chemical solution, specify which chemical species is being counted and balance its half-reaction before choosing $z$.

Michael Faraday's accessible 1834 paper, Experimental Researches in Electricity, Seventh Series, §783 states proportionality between chemical action and the quantity of electricity passed. In §§789–791 he describes connecting a molten tin-chloride cell in series with a water-decomposition charge indicator, weighing the receiving electrode before and after, and comparing the deposited metal with the indicator's gas readout. The common series electric current makes these two readouts comparable. This was a quantitative test of chemical equivalents, rather than merely an observation that a deposit appeared. It is historical evidence, not a suggested classroom procedure; the modern Electron-counting derivation above uses concepts unavailable to Faraday.^[ref]